Discovered it is possible to program a new remote from the DIC in a 2013.
it is not possible to do the same in a 2011.
I never looked, but today, on my 2007, when I was dicking around with my TPMS relearn after disconnecting my battery, I noticed I have an option on the DIC to do a remote relearn, along with the TPMS relearn. I wonder how the 2011 got left out?